H. Figueroa, Jose M. Gracia-Bondia, Joseph C. Varilly
{"title":"facomdi Bruno Hopf代数","authors":"H. Figueroa, Jose M. Gracia-Bondia, Joseph C. Varilly","doi":"10.15446/recolma.v56n1.105611","DOIUrl":null,"url":null,"abstract":"This is a short review on the Faà di Bruno formulas, implementing composition of real-analytic functions, and a Hopf algebra associated to such formulas. This structure provides, among several other things, a short proof of the Lie-Scheffers theorem, and relates the Lagrange inversion formulas with antipodes. It is also the maximal commutative Hopf subalgebra of the one used by Connes and Moscovici to study diffeomorphisms in a noncommutative geometry setting. The link of Faà di Bruno formulas with the theory of set partitions is developed in some detail.","PeriodicalId":38102,"journal":{"name":"Revista Colombiana de Matematicas","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2005-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Faà di Bruno Hopf algebras\",\"authors\":\"H. Figueroa, Jose M. Gracia-Bondia, Joseph C. Varilly\",\"doi\":\"10.15446/recolma.v56n1.105611\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This is a short review on the Faà di Bruno formulas, implementing composition of real-analytic functions, and a Hopf algebra associated to such formulas. This structure provides, among several other things, a short proof of the Lie-Scheffers theorem, and relates the Lagrange inversion formulas with antipodes. It is also the maximal commutative Hopf subalgebra of the one used by Connes and Moscovici to study diffeomorphisms in a noncommutative geometry setting. The link of Faà di Bruno formulas with the theory of set partitions is developed in some detail.\",\"PeriodicalId\":38102,\"journal\":{\"name\":\"Revista Colombiana de Matematicas\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-08-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista Colombiana de Matematicas\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15446/recolma.v56n1.105611\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Colombiana de Matematicas","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15446/recolma.v56n1.105611","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
This is a short review on the Faà di Bruno formulas, implementing composition of real-analytic functions, and a Hopf algebra associated to such formulas. This structure provides, among several other things, a short proof of the Lie-Scheffers theorem, and relates the Lagrange inversion formulas with antipodes. It is also the maximal commutative Hopf subalgebra of the one used by Connes and Moscovici to study diffeomorphisms in a noncommutative geometry setting. The link of Faà di Bruno formulas with the theory of set partitions is developed in some detail.
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